CONDENSED MATTER PHYSICS
Reception time
MONDAY 14-15 UFFICIO 147 EDIFICIO MARCONI
The course starts on
Wednesday 27/09/2023 in aula 4 Edificio Fermi
A.A: 2023/24. Teacher Marco
Grilli
Wednesday 8-10
Thursday12-14
Friday 15-16
Program
Crystal structures and Bravais lattice. Reciprocal
lattice. Diffraction and solid crystals, structure
factor. Born-Oppheneimer approximation. Lattice
vibrations, phonons, specific heat (Einstein's and
Debye's model, density of states). Electrons in
solids, Bloch's theorem,. Band structure. Tightly
and weakly bound electrons. Holes and effective
mass. Electrons in metals and interaction with an
electromagnetic field (dielectric response, metal
transport properties): Drude's and Sommerfeld's
models. Intrinsic and extrinsic semiconductors.
Temperature dependence of charge carrier density.
Adopted
texts
N.W. Ashcroft, N.D, Mermin, `Solid State Physics',
Holt-Saunders Int. Ed. 1981
C. Kittel, `Introduction to Solid Sate Physics', Wiley,
2004
J. M. Ziman, `Principles of the Theory of Solids',
Cambridge University Press, 1979
Prerequisites
The course relies on the following prerequisites:
1. CLASSICAL MECHANICS reference text: H. Goldstein, C. P.
Poole, and J. L. Safko Classical Mechanics, Addison-Wesley
chapter 1 Survey of elementary principles - mechanics of a
particle - mechanics of a system of particles - contraints
- D'Alambert's principle and Lagrange's equations chapter
6 Oscillations - formulation of the problem - the
eigenvalue equation and the principal axis transformation
- frequencies of free vibration and normal coordinates
chapter 8 The Hamilton equations of motion - Legendre
transformations and the Hamilton equations of motion
chapter 9 Canonical transformations - the equations of
canonical transformations - Poisson brackets - Liouville's
theorem
2. CLASSICAL ELECTROMAGNETISM reference text: D. Halliday,
R. Resnick, and K. S. Crane Physics - part II, John Wiley
& sons chapter 25 Electric charge and Coulomb's law -
electric charge - conductors and insulators - Coulomb's
law - continuous charge distributions - conservation of
charge chapter 26 The electric field - the electric field
- the electric field of point charges - the electric field
of continuous charge distributions chapter 27 Gauss' law -
the flux of the electric field - Gauss' law chapter 28
Electric potential energy and potential - electric
potential energy - electric potential - calculating the
potential from the field - potential due to point charges
- potential due to continuous charge distributions -
calculating the field from the potential - equipotential
surfaces - the potential of a charged conductor chapter 29
The electric properties of materials - types of materials
- a conductor in an alectric field - ohmic materials -
Ohm's law - an insultatori in an electric field chapter 30
Capacitance - capacitors - capacitance chapter 31 DC
circuits - electric current - electromotive force chapter
32 The magnetic field - the magnetic force on a moving
charge - circulating charges - the Hall effect
3. QUANTUM MECHANICS reference text: J. J. Sakurai Modern
Quantum Mechanics, Addison-Wesley chapter 1 Fundamental
concepts - kets, bras, operators - base kets and matrix
representation - measurements, observables, and
uncertainty relations - position, momentum, and
translation - wave functions in position and momentum
space chapter 2 Quantum dynamics - time evolution and the
Shroedinger equation - the Shroedinger versus the
Heisenberg picture - simple harmonic oscillator -
Schroedinger's wave equation chapter 3 Theory of angular
momentum - rotations and angular momentum commutation
relations - spin 1/2 systems and finite rotations -
eigenvalues and eigenstates of angular momentum - orbital
angular momentum - addition of angular momenta chapter 4
Symmetry in quantum mechanics - symmetries, conservation
laws, and degeneracies - discrete symmetries, parity, or
space inversion - lattice translation as a discrete
symmetry - the time-reversal discrete symmetry chapter 5
Approximation methods - time independent perturbation
theory: non degenerate case - time independent
perturbation theory: the degenerate case
4. STATISTICAL MECHANICS reference text: K. Huang
Statistical Mechanics, John Wiley & sons chapter 6
Classical statistical mechanics - the postulate of
classical statistical mechanics - microcanonical ensemble
- derivation of thermodynamics - equipartition theorem -
classical ideal gas chapter 7 Canonical ensemble and grand
canonical ensemble - canonical ensemble - energy
fluctuations in the canonical ensemble - grand canonical
ensemble - density fluctuations in the grand canonical
ensemble - the chemical potential - equivalence of the
canonical ensemble and grand canonical ensemble chapter 8
Quantum statistical mechanics - the postulate of quantum
statistical mechanics - ensembles in quantum statistical
mechanics - the ideal gases: micro canonical ensemble -
the ideal gases: grand canonical ensemble chapter 11 Fermi
systems - the equation of state of an ideal Fermi gas
chapter 12 Bose systems - photons - Bose-Einstein
condensation
5. ATOMIC AND MOLECULAR PHYSICS reference text: B. H
Bransden & C. J. Joachain Physics of atoms and
molecules, Longman Scientific & Technical chapter 3
One-electron atoms - the Scheoedinger equation for
one-electron atoms - energy levels - the eigenfunctions of
the bound states chapter 6 Two-electron atoms - the
Scheoedinger equation for two-electron atoms - spin wave
functions and the role of the Pauli exclusion principle -
level scheme of two-electron atoms chapter 7 Many-electron
atoms - the central field approximation - the periodic
system of the elements chapter 9 Molecular structure -
general nature of molecular structure - the
Born-Oppenheimer separation for diatomic molecules -
electronic structure of diatomic molecules - the structure
of polyatomic molecules
Study modes
The course includes lectures on the theory (amounting to
approximately 2/3 of the total number of hours dedicated
to lecturing), alternated with tutoring sessions
(amounting to approximately 1/3 of the total number of
hours dedicated to lecturing), during which the methods to
solve problems and exercises of the kinds that can be
assigned in a written exam are treated.
Frequency modes
Attendance to the lectures is not mandatory but strongly
recommended.
Exam modes
There are two mid-term assessment tests during the course
(lasting two hours each). If both tests are passed with a
score of at least 15/30 and an average of not less than
18/30, the student is exempted from the written test for
the entire academic year.
There are 5 complete calls (written and oral): two in the
January/February session, two in the June/July session and
one in the September session.
The written test (lasting three hours) includes two
problems, each one divided into several questions. The
written test is passed with a score of no less than 18/30
and is valid for the session in which it was taken.
The oral exam consists of an interview on the most
relevant topics presented in the course. To pass the exam,
the student must be able to present arguments and repeat
calculations discussed and explained during the course.
The student will be asked to apply the methods learned
during the course to exercises or to examples and
situations similar to those that were discussed in the
course.
The evaluation takes into account:
- Correctness and completeness of the concepts discussed
by the student;
- clarity and rigor of presentation;
- analytical development of the theory;
- problem-solving skills (method and results).
The final exam grade is determined by the average between
the written score (or the average of the mid-term
assessment tests) and the oral test score.
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Crystal structures, Bravais lattices, space groups [AM
ch.4, ch. 7] -Reciprocal lattice [AM ch. 5]
-Diffraction from crystals, structure factor [AM Ch. 6]
-Born-Oppenheimer approximation [Ziman p. 200]- Lattice
vibrations, phonons -Specific heat (Einstein and Debye
models, density of states) [AM-Ch. 22 p.421-443 and ch.
23]
-Electronic states and eigenvalues of polyatomic and
cyclic molecules - Electrons in solids, Bloch theorem -
Electronic bands - Nearly-free electrons - The
tight-binding method - [AM ch. 8-10]. The
concepts of holes and effective mass.
- Electrons in metals and interaction with the
elctromagnetic field (Dielectric function, transport
properties of metals): Drude model and Sommerfeld model
[AM ch. 1,2]. Semiclassical model.
- Intrinsic and extrinsic (doped) semiconductors - T
dependence of the number of charge carriers [AM cap. 28]
Optional topics:
Boltzmann equation (relaxation-time approx.) [Ziman,
Sec. 7.1,7.2]
Physics of the p-n junction and applications
to devices.
[AM ch. 29 p. 589-600].
Useful topics: AM B, C, D, E, F, L Appendices.
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References
- [AM]N.W. Ashcroft, N.D, Mermin, `Solid State Physics`,
Holt-Saunders Int. Ed. 1981.
- C. Kittel, `Introduzione alla Fisica dello Stato
Solido`, Ed. CEA, 2008.
- J.M. Ziman, `Principles of the Theory of Solids',
Cambridge University Press (1979)